The applicant proposes, in Japanese Laid-Open Patent Application No. Hei 10 (1998)-86081, conducting gait generation freely by converting a set of standard gaits, designed with the use of an off-line computer, into a set of time-series data including parameters and a body trajectory to be stored in a memory of a microcomputer mounted on a robot, and by calculating a weighted average of instantaneous values of individual gaits whose parameter relating to time such as a walking period are the same.
However, if a weighted average is calculated between individual gaits that are different in the time parameter such as the walking period, the generated gait does not satisfy the dynamic equilibrium condition even in an approximated manner. Thus, the proposed technique failed to generate a gait that is different from the standard gait in the walking period.
It should be noted here that the “dynamic equilibrium condition” indicates a situation where a ZMP determined from the gravity and inertial force of a desired gait is equal to a desired ZMP, to be more specifically, a situation where moment of the resultant force of the inertial force and gravity of the robot about the desired ZMP is zero. Here, the ZMP (Zero Moment Point) indicates a floor point at which the resultant force of the inertial force induced by motion and the gravity intersect the floor. More precisely, it indicates a point of action on the floor at which the moment of the resultant force of the inertial force induced by motion and gravity is zero except for its vertical component.
Further, in the proposed technique, since it is sometimes necessary to turn a desired ZMP away large from its expected trajectory so as to bring both the body position and velocity continuous at boundary of a gait of a walking step and that succeeding thereto, the margin of stability may occasionally lower.
Further, in order to realize various kinds of walking, the proposed technique requires a large number of standard gait time-series data to be stored and hence, needing an increased capacity of memory. Furthermore, a set of standard gaits must be prepared on an off-line computer by trial and error. In addition, when it is attempted to generate a gait that is quite different from the standard gait, the approximation is disadvantageously degraded markedly.
Aside from the above, since gait generation can not act against physical laws, gait parameters such as the ZMP should be determined within a permissible range of the physical laws. Moreover, assuming the dynamic system of a biped robot as a system that inputs the ZMP and outputs the body position, it is a divergence system. It therefore becomes necessary to prevent a behavior of robot from diverging by generated gait parameters. Here, “divergence” indicates, as shown in FIG. 8 referred to later, a body position of the biped robot deviates far away from its feet positions.
From this point of views, when generating gait on a real-time basis, it is preferable to predict future behavior that would occur in the robot by the generated gait, and to avoid divergence if the possibility of divergence is predicted.
However, as shown in FIG. 23, when a robot (biped robot) is modeled to have multiple material points, since the volume of calculation and the non-linearity of system increase, it is difficult for an on-board computer (mounted on the robot of ordinary performance) to determine gait terminal state on a real-time basis.
As regards the future behavior prediction and divergence prevention technique based thereon might be realized to a certain level, by, for example, storing various kinds of knowledge and by selecting a desired gait at every gait switching in response to the state and objective at that time from the stored knowledge. In practice, however, a trial to cope with all possible condition would cause an explosion of combination, and this method would actually be impossible.
Therefore, it is desired in the field of legged mobile robot technology to simplify a dynamic model that describes the robot dynamics in such a way that robot's future behavior can analytically be predicated in calculation on a real-time basis.
As typical robot dynamic models, following two models are known.
1) a model assigned with a single material point.
2) a model assigned with multiple material points (but, material points with less influence are neglected).
The single-material-point model of 1) is proposed in Japanese Patent Publication Hei 4 (1992)-15068. In the proposed technique, the robot is model as a single-material-point model in which the material point is only set at its body to ensure linearity such that it is controlled the body height to be constant. This model makes it easy to determine robot behavior analytically.
Since the biped robot in the proposed technique is quite small in weight, the leg reaction force can be neglected without leaving significant influence to exist. However, in case of a biped robot of humanoid type, since the mass of its leg is so large that it can not be neglected, if the proposed technique is adopted to the humanoid type robot, the accuracy of approximation will accordingly be degraded and the robot may, at worse, turn over if controlled to walk at a high speed.
As an example of the model of 2), it can be cited a model described in a paper “Biped Walking Control Method Adapting to an Unknown Uneven Surface” (Journal of the Robotics Society of Japan; Vol. 13 No. 7; October, 1995).
In the proposed technique, the material points are set on knees and ankles of each leg and on the body. More specifically, the individual material points are set on fixed points (coordinate) in coordinate systems set locally on its links and joints. When comparing this model with that shown in FIG. 23 (in which the material points and inertia are set at every link), the model of 2) can decrease the volume of calculation to {fraction (1/10)} or thereabout. In addition, the accuracy of approximation of the model of 2) will be improved than the model of 1) and even a robot having a large-mass leg can walk in accordance with gaits generated by the technique mentioned in the paper.
However, since the non-linearity in the model of 2) is still excessive, like the model shown in FIG. 23, it is not possible to use the model of 2) for predicting future behavior analytically so as to avoid divergence.